which are called graph filters [1]}, [2]}. For a given input \(\mathbf {x}\) , the output of the filter is simply \(\mathbf {y}=\mathbf {H}\mathbf {x}\) . The coefficients of the filter are collected into \(\mathbf {h}:=[h_0,\ldots ,h_{\text{L}-1}]^\text{T}\) , with \(\text{L}-1\)  denoting the filter degree. Graph filters are of particular interest because they model network diffusion processes and can be implemented in a distributed fashion [2]}, [4]}.
Note also that the Cayley-Hamilton theorem guarantees that even infinite-horizon processes (i.e., those depending on arbitrarily large powers of \(\mathbf {S}\) ) can be rewritten as a filter of at most degree \(\text{N}-1\) .
